Formalizing reflective inconsistency

3 Johnicholas 13 September 2009 04:23AM

In the post Outlawing Anthropics, there was a brief and intriguing scrap of reasoning, which used the principle of reflective inconsistency, which so far as I know is unique to this community:

If your current system cares about yourself and your future, but doesn't care about very similar xerox-siblings, then you will tend to self-modify to have future copies of yourself care about each other, as this maximizes your expectation of pleasant experience over future selves.

This post expands upon and attempts to formalize that reasoning, in hopes of developing a logical framework for reasoning about reflective inconsistency.

continue reading »

Formalizing informal logic

12 Johnicholas 10 September 2009 08:16PM

As an exercise, I take a scrap of argumentation, expand it into a tree diagram (using FreeMind), and then formalize the argument (in Automath). This towards the goal of creating  "rationality augmentation" software. In the short term, my suspicion is that such software would look like a group of existing tools glued together with human practices.

About my choice of tools: I investigated Araucaria, Rationale, Argumentative, and Carneades. With the exception of Rationale, they're not as polished graphically as FreeMind, and the rigid argumentation-theory structure was annoying in the early stages of analysis. Using a general-purpose mapping/outlining tool may not be ideal, but it's easy to obtain. The primary reason I used Automath to formalize the argument was because I'm somewhat familiar with it. Another reason is that it's easy to obtain and build (at least, on GNU/Linux).

Automath is an ancient and awesomely flexible proof checker. (Of course, other more modern proof-checkers are often just as flexible, maybe more flexible, and may be more useable.) The amount of "proof checking" done in this example is trivial - roughly, what the checker is checking is: "after assuming all of these bits and pieces of opaque human reasoning, do they form some sort of tree?" - but cutting down a powerful tool leaves a nice upgrade path, in case people start using exotic forms of logic.  However, the argument checkers built into the various argumentation-theory tools do not have such upgrade paths, and so are not really credible as candidates to formalize the arguments on this site.

continue reading »